Quantum systems are typically subject to various environmental noise sources. Treating these environmental disturbances with a system-bath approach beyond weak coupling, one must refer to numerical methods as, for example, the numerically exact quasi-adiabatic path integral approach. This approach, however, cannot treat baths which couple to the system via operators, which do not commute. We extend the quasi-adiabatic path integral approach by determining the time discrete influence functional for such non-commuting fluctuations and by modifying the propagation scheme accordingly. We test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent baths via non-commuting operators. We show that the convergent results can be obtained and agreement with the analytical weak coupling results is achieved in the respective limits.

We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher-order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e., even many-body systems.

Recent experimental results showing atypical nonlinear absorption and marked deviations from well known universality in the low temperature acoustic and dielectric losses in amorphous solids prove the need for improving the understanding of the nature of two-level systems (TLSs) in these materials. Here we suggest the study of TLSs focused on their properties which are nonuniversal. Our theoretical analysis shows that the standard tunneling model and the recently suggested two-TLS model provide markedly different predictions for the experimental outcome of these studies. Our results may be directly tested in disordered lattices, e.g KBr:CN, where there is ample theoretical support for the validity of the two-TLS model, as well as in amorphous solids. Verification of our results in the latter will significantly enhance understanding of the nature of TLSs in amorphous solids, and the ability to manipulate them and reduce their destructive effect in various cutting edge applications including superconducting qubits.

Environmental rocking ratchet: Environmental rectification by a harmonically driven avoided crossing
(2017)

We propose a rocking ratchet designed as a symmetric quantum two-state system driven by a single periodic harmonic force and influenced symmetrically by thermal fluctuations. We show that the necessary broken symmetry can dynamically be achieved by a thermal environment that couples to the energy difference between the two states and the tunnel coupling between them. The quantum two-state system is driven by the harmonic periodic drive through its avoided crossing. The correspondingly driven dissipative quantum dynamics results on average in a finite population difference between both states. This then causes directed particle transport.

Environmental noise leads to dephasing and relaxation in a quantum system. Often, a rigorous treatment of multiple noise sources within a system-bath approach is not possible. We discuss the influence of environmental fluctuations on a quantum system whose dynamics is dephasing already due to a phenomenologically treated additional noise source. For this situation, we develop a path-integral approach, which allows us to treat the system-environment coupling in a numerically exact way, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerically exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative.

The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.

Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. Wefind that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect-phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect-phonon coupling. This allows direct experimental determination of the defect-phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.

We present a scheme for cooling a vibrational mode of a magnetic molecular nanojunction by a spin-polarized charge current upon exploiting the interaction between its magnetic moment and the vibration. The spin-polarized charge current polarizes the magnetic moment of the nanoisland, thereby lowering its energy. A small but finite coupling between the vibration and the magnetic moment permits a direct exchange of energy such that vibrational energy can be transferred into the magnetic state. For positive bias voltages, this generates an effective cooling of the molecular vibrational mode. We determine parameter regimes for the cooling of the vibration to be optimal. Although the flowing charge current inevitably heats up the vibrational mode via Ohmic energy losses, we show that due to the magnetomechanical coupling, the vibrational energy (i.e, the effective phonon temperature) can be lowered below 50% of its initial value, when the two leads are polarized anti-parallel. In contrast to the cooling effect for positive bias voltages, net heating of the vibrational mode occurs for negative bias voltages. The cooling effect is enhanced for a stronger anti-parallel magnetic polarization of the leads, while the heating is stronger for a larger parallel polarization. Yet, dynamical cooling is also possible with parallel lead alignments when the two tunneling barriers are asymmetric.